title: Intrinsic Regression Models for Medial Representation of Subcortical Structures.
abstract: The aim of this paper is to develop a semiparametric model for describing the variability of the medial representation of subcortical structures, which belongs to a Riemannian manifold, and establishing its association with covariates of interest, such as diagnostic status, age and gender. We develop a two-stage estimation procedure to calculate the parameter estimates. The first stage is to calculate an intrinsic least squares estimator of the parameter vector using the annealing evolutionary stochastic approximation Monte Carlo algorithm and then the second stage is to construct a set of estimating equations to obtain a more efficient estimate with the intrinsic least squares estimate as the starting point. We use Wald statistics to test linear hypotheses of unknown parameters and establish their limiting distributions. Simulation studies are used to evaluate the accuracy of our parameter estimates and the finite sample performance of the Wald statistics. We apply our methods to the detection of the difference in the morphological changes of the left and right hippocampi between schizophrenia patients and healthy controls using medial shape description.
authors.affiliation: H. Zhu is Professor of Biostatistics ( hzhu@bios.unc.edu ), J. G. Ibrahim is Alumni Distinguished Professor of Biostatistics ( ibrahim@bios.unc.edu ), and X. Shi was Ph.d student ( amy.shi@sas.com ), Department of Biostatistics and Biomedical Research Imaging Center, University of North Carolina at Chapel Hill, NC 27599-7420. F. Liang is Professor of Statistics ( fliang@stat.tamu.edu ), Department of Statistics, Texas A & M University, College Station, TX 77843-3143. Jeffrey Lieberman is Lawrence C. Kolb Professor of Psychiatry ( jlieberman@pi.cpmc.Columbia.edu ), Department of Psychiatry, Columbia University Medical Center, 1051 Riverside Drive, New York, New York 10032, U.S.A. M. Styner is Assistant Professor ( yasheng.chen@med.unc.edu ), Department of Computer Science and Psychiatry, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599.
authors.forename: Xiaoyan
authors.initials: X
authors.lastname: Shi
authors.forename: Hongtu
authors.initials: H
authors.lastname: Zhu
authors.forename: Joseph G
authors.initials: JG
authors.lastname: Ibrahim
authors.forename: Faming
authors.initials: F
authors.lastname: Liang
authors.forename: Jeffrey
authors.initials: J
authors.lastname: Lieberman
authors.forename: Martin
authors.initials: M
authors.lastname: Styner
keywords: Intrinsic least squares estimator; Medial representation; Semiparametric model; Wald statistic